Gray-Scott Reaction-Diffusion HPC Summer School Project

Research question

How do local reaction terms and diffusion generate spatial patterns, and how does implementation strategy affect simulation scale, stability, and reproducibility?

Background

The Gray-Scott model is a useful reproduction project because it has recognizable qualitative outputs and clear numerical challenges. It also fits the summer-school HPC context: the same mathematical model can be implemented naively, vectorised, or parallelised, making performance and numerical validation visible.

Mathematical model

The model tracks two concentration fields, feed and kill parameters, diffusion coefficients, boundary conditions, and an initial perturbation. The core numerical issue is the interaction between discretisation choices, timestep stability, grid size, and the qualitative patterns produced.

Methods

The project will document the finite-difference scheme, grid resolution, timestep, boundary treatment, parameter sweep strategy, and runtime behaviour. It should separate attractive visual output from validated numerical output.

Implementation

The implementation is being organised around reproducible runs: a single command should generate figures, save parameter settings, and make it possible to compare CPU/vectorised/HPC variants.

Results

Show selected patterns, explain parameter regimes, and avoid presenting attractive images without interpretation.

Validation

Check grid refinement, timestep stability, mass behavior, and comparison with known qualitative parameter regions.

Limitations

Pattern similarity is not full validation. The page should be honest about numerical artifacts and model idealization.

What I learned

This project can demonstrate PDE discretization, stability constraints, scientific visualization, and reproducible simulation practice.

Future work

Potential extensions include GPU acceleration, interactive parameter exploration, and comparison with other reaction-diffusion models.